Problem: The sum of two integers is $75$. One of the numbers is three more than the other. What is the larger integer?
Solution: If $x$ is the larger integer, then the smaller integer is $x-3$. We find the sum and set it equal to 75: $$x+x-3=75 \Rightarrow   2x=78 \Rightarrow   x=39$$ The larger integer is $\boxed{39}$.